What are the solutions to the equation x^3-2x=1 ?

The solutions to the equation x^3-2x=1 are x=-1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of x^3-2x=1

The zeros of x^3-2x=1 are x=-1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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x^{3} - 2 x = 1

x = - 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = - 1, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

x^{3} - 2 x = 1

Move

1

to the left side

x^{3} - 2 x - 1 = 0

Factor

x^{3} - 2 x - 1 : (x + 1) (x^{2} - x - 1)

(x + 1) (x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - x - 1 = 0 : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

The solutions are

x = - 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

R, T^{2} = R^{3}

(x - 1)^{4} + 2 (x - 1)^{2} - 3 = 0

(6 x + 7)^{2} (3 x + 4) (x + 1) = 6

x^{5} - x^{4} - 3 x^{3} + 5 x^{2} - 2 x = 0

2 x^{3} - 8 x^{2} + 2 x + 12 = 0

What are the solutions to the equation x^3-2x=1 ?
The solutions to the equation x^3-2x=1 are x=-1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of x^3-2x=1
The zeros of x^3-2x=1 are x=-1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2